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ftu/blst/asm/ct_inverse_mod_256-armv8.pl
John Doe 943c07066e initial stuff
2022-09-09 02:47:49 -04:00

587 lines
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Raku
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#!/usr/bin/env perl
#
# Copyright Supranational LLC
# Licensed under the Apache License, Version 2.0, see LICENSE for details.
# SPDX-License-Identifier: Apache-2.0
#
# Both constant-time and fast Euclidean inversion as suggested in
# https://eprint.iacr.org/2020/972. ~4.600 cycles on Apple M1, ~8.900 -
# on Cortex-A57.
#
# void ct_inverse_mod_256(vec512 ret, const vec256 inp, const vec256 mod,
# const vec256 modx);
#
$python_ref.=<<'___';
def ct_inverse_mod_256(inp, mod):
a, u = inp, 1
b, v = mod, 0
k = 31
mask = (1 << k) - 1
for i in range(0, 512 // k - 1):
# __ab_approximation_31
n = max(a.bit_length(), b.bit_length())
if n < 64:
a_, b_ = a, b
else:
a_ = (a & mask) | ((a >> (n-k-2)) << k)
b_ = (b & mask) | ((b >> (n-k-2)) << k)
# __inner_loop_31
f0, g0, f1, g1 = 1, 0, 0, 1
for j in range(0, k):
if a_ & 1:
if a_ < b_:
a_, b_, f0, g0, f1, g1 = b_, a_, f1, g1, f0, g0
a_, f0, g0 = a_-b_, f0-f1, g0-g1
a_, f1, g1 = a_ >> 1, f1 << 1, g1 << 1
# __smul_256_n_shift_by_31
a, b = (a*f0 + b*g0) >> k, (a*f1 + b*g1) >> k
if a < 0:
a, f0, g0 = -a, -f0, -g0
if b < 0:
b, f1, g1 = -b, -f1, -g1
# __smul_512x63
u, v = u*f0 + v*g0, u*f1 + v*g1
if 512 % k + k:
f0, g0, f1, g1 = 1, 0, 0, 1
for j in range(0, 512 % k + k):
if a & 1:
if a < b:
a, b, f0, g0, f1, g1 = b, a, f1, g1, f0, g0
a, f0, g0 = a-b, f0-f1, g0-g1
a, f1, g1 = a >> 1, f1 << 1, g1 << 1
v = u*f1 + v*g1
mod <<= 512 - mod.bit_length() # align to the left
if v < 0:
v += mod
if v < 0:
v += mod
elif v == 1<<512
v -= mod
return v & (2**512 - 1) # to be reduced % mod
___
$flavour = shift;
$output = shift;
if ($flavour && $flavour ne "void") {
$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or
( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or
die "can't locate arm-xlate.pl";
open STDOUT,"| \"$^X\" $xlate $flavour $output";
} else {
open STDOUT,">$output";
}
my ($out_ptr, $in_ptr, $n_ptr, $nx_ptr) = map("x$_", (0..3));
my @acc=map("x$_",(4..11));
my ($f0, $g0, $f1, $g1, $f_, $g_) = map("x$_",(12..17));
my $cnt = $n_ptr;
my @t = map("x$_",(19..26));
my ($a_lo, $b_lo) = @acc[3,7];
$frame = 16+2*512;
$code.=<<___;
.text
.globl ct_inverse_mod_256
.type ct_inverse_mod_256, %function
.align 5
ct_inverse_mod_256:
paciasp
stp x29, x30, [sp,#-80]!
add x29, sp, #0
stp x19, x20, [sp,#16]
stp x21, x22, [sp,#32]
stp x23, x24, [sp,#48]
stp x25, x26, [sp,#64]
sub sp, sp, #$frame
ldp @acc[0], @acc[1], [$in_ptr,#8*0]
ldp @acc[2], @acc[3], [$in_ptr,#8*2]
add $in_ptr, sp, #16+511 // find closest 512-byte-aligned spot
and $in_ptr, $in_ptr, #-512 // in the frame...
str $out_ptr, [sp]
ldp @acc[4], @acc[5], [$n_ptr,#8*0]
ldp @acc[6], @acc[7], [$n_ptr,#8*2]
stp @acc[0], @acc[1], [$in_ptr,#8*0] // copy input to |a|
stp @acc[2], @acc[3], [$in_ptr,#8*2]
stp @acc[4], @acc[5], [$in_ptr,#8*4] // copy modulus to |b|
stp @acc[6], @acc[7], [$in_ptr,#8*6]
////////////////////////////////////////// first iteration
bl .Lab_approximation_31_256_loaded
eor $out_ptr, $in_ptr, #256 // pointer to dst |a|b|u|v|
bl __smul_256_n_shift_by_31
str $f0,[$out_ptr,#8*8] // initialize |u| with |f0|
mov $f0, $f1 // |f1|
mov $g0, $g1 // |g1|
add $out_ptr, $out_ptr, #8*4 // pointer to dst |b|
bl __smul_256_n_shift_by_31
str $f0, [$out_ptr,#8*9] // initialize |v| with |f1|
////////////////////////////////////////// second iteration
eor $in_ptr, $in_ptr, #256 // flip-flop src |a|b|u|v|
bl __ab_approximation_31_256
eor $out_ptr, $in_ptr, #256 // pointer to dst |a|b|u|v|
bl __smul_256_n_shift_by_31
mov $f_, $f0 // corrected |f0|
mov $g_, $g0 // corrected |g0|
mov $f0, $f1 // |f1|
mov $g0, $g1 // |g1|
add $out_ptr, $out_ptr, #8*4 // pointer to destination |b|
bl __smul_256_n_shift_by_31
ldr @acc[4], [$in_ptr,#8*8] // |u|
ldr @acc[5], [$in_ptr,#8*13] // |v|
madd @acc[0], $f_, @acc[4], xzr // |u|*|f0|
madd @acc[0], $g_, @acc[5], @acc[0] // |v|*|g0|
str @acc[0], [$out_ptr,#8*4]
asr @acc[1], @acc[0], #63 // sign extenstion
stp @acc[1], @acc[1], [$out_ptr,#8*5]
stp @acc[1], @acc[1], [$out_ptr,#8*7]
madd @acc[0], $f0, @acc[4], xzr // |u|*|f1|
madd @acc[0], $g0, @acc[5], @acc[0] // |v|*|g1|
str @acc[0], [$out_ptr,#8*9]
asr @acc[1], @acc[0], #63 // sign extenstion
stp @acc[1], @acc[1], [$out_ptr,#8*10]
stp @acc[1], @acc[1], [$out_ptr,#8*12]
___
for($i=2; $i<15; $i++) {
$code.=<<___;
eor $in_ptr, $in_ptr, #256 // flip-flop src |a|b|u|v|
bl __ab_approximation_31_256
eor $out_ptr, $in_ptr, #256 // pointer to dst |a|b|u|v|
bl __smul_256_n_shift_by_31
mov $f_, $f0 // corrected |f0|
mov $g_, $g0 // corrected |g0|
mov $f0, $f1 // |f1|
mov $g0, $g1 // |g1|
add $out_ptr, $out_ptr, #8*4 // pointer to destination |b|
bl __smul_256_n_shift_by_31
add $out_ptr, $out_ptr, #8*4 // pointer to destination |u|
bl __smul_256x63
adc @t[3], @t[3], @t[4]
str @t[3], [$out_ptr,#8*4]
mov $f_, $f0 // corrected |f1|
mov $g_, $g0 // corrected |g1|
add $out_ptr, $out_ptr, #8*5 // pointer to destination |v|
bl __smul_256x63
___
$code.=<<___ if ($i>7);
bl __smul_512x63_tail
___
$code.=<<___ if ($i<=7);
adc @t[3], @t[3], @t[4]
stp @t[3], @t[3], [$out_ptr,#8*4]
stp @t[3], @t[3], [$out_ptr,#8*6]
___
}
$code.=<<___;
////////////////////////////////////////// two[!] last iterations
eor $in_ptr, $in_ptr, #256 // flip-flop src |a|b|u|v|
mov $cnt, #47 // 31 + 512 % 31
//bl __ab_approximation_62_256 // |a| and |b| are exact,
ldr $a_lo, [$in_ptr,#8*0] // just load
ldr $b_lo, [$in_ptr,#8*4]
bl __inner_loop_62_256
mov $f_, $f1
mov $g_, $g1
ldr $out_ptr, [sp] // original out_ptr
bl __smul_256x63
bl __smul_512x63_tail
ldr x30, [x29,#8]
smulh @t[1], @acc[3], $g_ // figure out top-most limb
ldp @acc[4], @acc[5], [$nx_ptr,#8*0]
adc @t[4], @t[4], @t[6]
ldp @acc[6], @acc[7], [$nx_ptr,#8*2]
add @t[1], @t[1], @t[4] // @t[1] is 1, 0 or -1
asr @t[0], @t[1], #63 // sign as mask
and @t[4], @acc[4], @t[0] // add mod<<256 conditionally
and @t[5], @acc[5], @t[0]
adds @acc[0], @acc[0], @t[4]
and @t[6], @acc[6], @t[0]
adcs @acc[1], @acc[1], @t[5]
and @t[7], @acc[7], @t[0]
adcs @acc[2], @acc[2], @t[6]
adcs @acc[3], @t[3], @t[7]
adc @t[1], @t[1], xzr // @t[1] is 1, 0 or -1
neg @t[0], @t[1]
orr @t[1], @t[1], @t[0] // excess bit or sign as mask
asr @t[0], @t[0], #63 // excess bit as mask
and @acc[4], @acc[4], @t[1] // mask |mod|
and @acc[5], @acc[5], @t[1]
and @acc[6], @acc[6], @t[1]
and @acc[7], @acc[7], @t[1]
eor @acc[4], @acc[4], @t[0] // conditionally negate |mod|
eor @acc[5], @acc[5], @t[0]
adds @acc[4], @acc[4], @t[0], lsr#63
eor @acc[6], @acc[6], @t[0]
adcs @acc[5], @acc[5], xzr
eor @acc[7], @acc[7], @t[0]
adcs @acc[6], @acc[6], xzr
adc @acc[7], @acc[7], xzr
adds @acc[0], @acc[0], @acc[4] // final adjustment for |mod|<<256
adcs @acc[1], @acc[1], @acc[5]
adcs @acc[2], @acc[2], @acc[6]
stp @acc[0], @acc[1], [$out_ptr,#8*4]
adc @acc[3], @acc[3], @acc[7]
stp @acc[2], @acc[3], [$out_ptr,#8*6]
add sp, sp, #$frame
ldp x19, x20, [x29,#16]
ldp x21, x22, [x29,#32]
ldp x23, x24, [x29,#48]
ldp x25, x26, [x29,#64]
ldr x29, [sp],#80
autiasp
ret
.size ct_inverse_mod_256,.-ct_inverse_mod_256
////////////////////////////////////////////////////////////////////////
.type __smul_256x63, %function
.align 5
__smul_256x63:
___
for($j=0; $j<2; $j++) {
my $f_ = $f_; $f_ = $g_ if ($j);
my @acc = @acc; @acc = @acc[4..7] if ($j);
my $k = 8*8+8*5*$j;
$code.=<<___;
ldp @acc[0], @acc[1], [$in_ptr,#8*0+$k] // load |u| (or |v|)
asr $f1, $f_, #63 // |f_|'s sign as mask (or |g_|'s)
ldp @acc[2], @acc[3], [$in_ptr,#8*2+$k]
eor $f_, $f_, $f1 // conditionally negate |f_| (or |g_|)
ldr @t[3+$j], [$in_ptr,#8*4+$k]
eor @acc[0], @acc[0], $f1 // conditionally negate |u| (or |v|)
sub $f_, $f_, $f1
eor @acc[1], @acc[1], $f1
adds @acc[0], @acc[0], $f1, lsr#63
eor @acc[2], @acc[2], $f1
adcs @acc[1], @acc[1], xzr
eor @acc[3], @acc[3], $f1
adcs @acc[2], @acc[2], xzr
eor @t[3+$j], @t[3+$j], $f1
umulh @t[0], @acc[0], $f_
adcs @acc[3], @acc[3], xzr
umulh @t[1], @acc[1], $f_
adcs @t[3+$j], @t[3+$j], xzr
umulh @t[2], @acc[2], $f_
___
$code.=<<___ if ($j!=0);
adc $g1, xzr, xzr // used in __smul_512x63_tail
___
$code.=<<___;
mul @acc[0], @acc[0], $f_
cmp $f_, #0
mul @acc[1], @acc[1], $f_
csel @t[3+$j], @t[3+$j], xzr, ne
mul @acc[2], @acc[2], $f_
adds @acc[1], @acc[1], @t[0]
mul @t[5+$j], @acc[3], $f_
adcs @acc[2], @acc[2], @t[1]
adcs @t[5+$j], @t[5+$j], @t[2]
___
$code.=<<___ if ($j==0);
adc @t[7], xzr, xzr
___
}
$code.=<<___;
adc @t[7], @t[7], xzr
adds @acc[0], @acc[0], @acc[4]
adcs @acc[1], @acc[1], @acc[5]
adcs @acc[2], @acc[2], @acc[6]
stp @acc[0], @acc[1], [$out_ptr,#8*0]
adcs @t[5], @t[5], @t[6]
stp @acc[2], @t[5], [$out_ptr,#8*2]
ret
.size __smul_256x63,.-__smul_256x63
.type __smul_512x63_tail, %function
.align 5
__smul_512x63_tail:
umulh @t[5], @acc[3], $f_
ldp @acc[1], @acc[2], [$in_ptr,#8*18] // load rest of |v|
adc @t[7], @t[7], xzr
ldr @acc[3], [$in_ptr,#8*20]
and @t[3], @t[3], $f_
umulh @acc[7], @acc[7], $g_ // resume |v|*|g1| chain
sub @t[5], @t[5], @t[3] // tie up |u|*|f1| chain
asr @t[6], @t[5], #63
eor @acc[1], @acc[1], $f1 // conditionally negate rest of |v|
eor @acc[2], @acc[2], $f1
adds @acc[1], @acc[1], $g1
eor @acc[3], @acc[3], $f1
adcs @acc[2], @acc[2], xzr
umulh @t[0], @t[4], $g_
adc @acc[3], @acc[3], xzr
umulh @t[1], @acc[1], $g_
add @acc[7], @acc[7], @t[7]
umulh @t[2], @acc[2], $g_
mul @acc[0], @t[4], $g_
mul @acc[1], @acc[1], $g_
adds @acc[0], @acc[0], @acc[7]
mul @acc[2], @acc[2], $g_
adcs @acc[1], @acc[1], @t[0]
mul @t[3], @acc[3], $g_
adcs @acc[2], @acc[2], @t[1]
adcs @t[3], @t[3], @t[2]
adc @t[4], xzr, xzr // used in the final step
adds @acc[0], @acc[0], @t[5]
adcs @acc[1], @acc[1], @t[6]
adcs @acc[2], @acc[2], @t[6]
stp @acc[0], @acc[1], [$out_ptr,#8*4]
adcs @t[3], @t[3], @t[6] // carry is used in the final step
stp @acc[2], @t[3], [$out_ptr,#8*6]
ret
.size __smul_512x63_tail,.-__smul_512x63_tail
.type __smul_256_n_shift_by_31, %function
.align 5
__smul_256_n_shift_by_31:
___
for($j=0; $j<2; $j++) {
my $f0 = $f0; $f0 = $g0 if ($j);
my @acc = @acc; @acc = @acc[4..7] if ($j);
my $k = 8*4*$j;
$code.=<<___;
ldp @acc[0], @acc[1], [$in_ptr,#8*0+$k] // load |a| (or |b|)
asr @t[5], $f0, #63 // |f0|'s sign as mask (or |g0|'s)
ldp @acc[2], @acc[3], [$in_ptr,#8*2+$k]
eor @t[6], $f0, @t[5] // conditionally negate |f0| (or |g0|)
eor @acc[0], @acc[0], @t[5] // conditionally negate |a| (or |b|)
sub @t[6], @t[6], @t[5]
eor @acc[1], @acc[1], @t[5]
adds @acc[0], @acc[0], @t[5], lsr#63
eor @acc[2], @acc[2], @t[5]
adcs @acc[1], @acc[1], xzr
eor @acc[3], @acc[3], @t[5]
umulh @t[0], @acc[0], @t[6]
adcs @acc[2], @acc[2], xzr
umulh @t[1], @acc[1], @t[6]
adc @acc[3], @acc[3], xzr
umulh @t[2], @acc[2], @t[6]
and @t[5], @t[5], @t[6]
umulh @t[3+$j], @acc[3], @t[6]
neg @t[5], @t[5]
mul @acc[0], @acc[0], @t[6]
mul @acc[1], @acc[1], @t[6]
mul @acc[2], @acc[2], @t[6]
adds @acc[1], @acc[1], @t[0]
mul @acc[3], @acc[3], @t[6]
adcs @acc[2], @acc[2], @t[1]
adcs @acc[3], @acc[3], @t[2]
adc @t[3+$j], @t[3+$j], @t[5]
___
}
$code.=<<___;
adds @acc[0], @acc[0], @acc[4]
adcs @acc[1], @acc[1], @acc[5]
adcs @acc[2], @acc[2], @acc[6]
adcs @acc[3], @acc[3], @acc[7]
adc @acc[4], @t[3], @t[4]
extr @acc[0], @acc[1], @acc[0], #31
extr @acc[1], @acc[2], @acc[1], #31
extr @acc[2], @acc[3], @acc[2], #31
asr @t[4], @acc[4], #63 // result's sign as mask
extr @acc[3], @acc[4], @acc[3], #31
eor @acc[0], @acc[0], @t[4] // ensure the result is positive
eor @acc[1], @acc[1], @t[4]
adds @acc[0], @acc[0], @t[4], lsr#63
eor @acc[2], @acc[2], @t[4]
adcs @acc[1], @acc[1], xzr
eor @acc[3], @acc[3], @t[4]
adcs @acc[2], @acc[2], xzr
stp @acc[0], @acc[1], [$out_ptr,#8*0]
adc @acc[3], @acc[3], xzr
stp @acc[2], @acc[3], [$out_ptr,#8*2]
eor $f0, $f0, @t[4] // adjust |f/g| accordingly
eor $g0, $g0, @t[4]
sub $f0, $f0, @t[4]
sub $g0, $g0, @t[4]
ret
.size __smul_256_n_shift_by_31,.-__smul_256_n_shift_by_31
___
{
my @a = @acc[0..3];
my @b = @acc[4..7];
my ($fg0, $fg1, $bias) = ($g0, $g1, @t[4]);
$code.=<<___;
.type __ab_approximation_31_256, %function
.align 4
__ab_approximation_31_256:
ldp @a[2], @a[3], [$in_ptr,#8*2]
ldp @b[2], @b[3], [$in_ptr,#8*6]
ldp @a[0], @a[1], [$in_ptr,#8*0]
ldp @b[0], @b[1], [$in_ptr,#8*4]
.Lab_approximation_31_256_loaded:
orr @t[0], @a[3], @b[3] // check top-most limbs, ...
cmp @t[0], #0
csel @a[3], @a[3], @a[2], ne
csel @b[3], @b[3], @b[2], ne
csel @a[2], @a[2], @a[1], ne
orr @t[0], @a[3], @b[3] // and ones before top-most, ...
csel @b[2], @b[2], @b[1], ne
cmp @t[0], #0
csel @a[3], @a[3], @a[2], ne
csel @b[3], @b[3], @b[2], ne
csel @a[2], @a[2], @a[0], ne
orr @t[0], @a[3], @b[3] // and one more, ...
csel @b[2], @b[2], @b[0], ne
clz @t[0], @t[0]
cmp @t[0], #64
csel @t[0], @t[0], xzr, ne
csel @a[3], @a[3], @a[2], ne
csel @b[3], @b[3], @b[2], ne
neg @t[1], @t[0]
lslv @a[3], @a[3], @t[0] // align high limbs to the left
lslv @b[3], @b[3], @t[0]
lsrv @a[2], @a[2], @t[1]
lsrv @b[2], @b[2], @t[1]
and @a[2], @a[2], @t[1], asr#6
and @b[2], @b[2], @t[1], asr#6
orr $a_lo, @a[3], @a[2]
orr $b_lo, @b[3], @b[2]
bfxil $a_lo, @a[0], #0, #31
bfxil $b_lo, @b[0], #0, #31
b __inner_loop_31_256
ret
.size __ab_approximation_31_256,.-__ab_approximation_31_256
.type __inner_loop_31_256, %function
.align 4
__inner_loop_31_256:
mov $cnt, #31
mov $fg0, #0x7FFFFFFF80000000 // |f0|=1, |g0|=0
mov $fg1, #0x800000007FFFFFFF // |f1|=0, |g1|=1
mov $bias,#0x7FFFFFFF7FFFFFFF
.Loop_31_256:
sbfx @t[3], $a_lo, #0, #1 // if |a_| is odd, then we'll be subtracting
sub $cnt, $cnt, #1
and @t[0], $b_lo, @t[3]
sub @t[1], $b_lo, $a_lo // |b_|-|a_|
subs @t[2], $a_lo, @t[0] // |a_|-|b_| (or |a_|-0 if |a_| was even)
mov @t[0], $fg1
csel $b_lo, $b_lo, $a_lo, hs // |b_| = |a_|
csel $a_lo, @t[2], @t[1], hs // borrow means |a_|<|b_|, replace with |b_|-|a_|
csel $fg1, $fg1, $fg0, hs // exchange |fg0| and |fg1|
csel $fg0, $fg0, @t[0], hs
lsr $a_lo, $a_lo, #1
and @t[0], $fg1, @t[3]
and @t[1], $bias, @t[3]
sub $fg0, $fg0, @t[0] // |f0|-=|f1| (or |f0-=0| if |a_| was even)
add $fg1, $fg1, $fg1 // |f1|<<=1
add $fg0, $fg0, @t[1]
sub $fg1, $fg1, $bias
cbnz $cnt, .Loop_31_256
mov $bias, #0x7FFFFFFF
ubfx $f0, $fg0, #0, #32
ubfx $g0, $fg0, #32, #32
ubfx $f1, $fg1, #0, #32
ubfx $g1, $fg1, #32, #32
sub $f0, $f0, $bias // remove bias
sub $g0, $g0, $bias
sub $f1, $f1, $bias
sub $g1, $g1, $bias
ret
.size __inner_loop_31_256,.-__inner_loop_31_256
.type __inner_loop_62_256, %function
.align 4
__inner_loop_62_256:
mov $f0, #1 // |f0|=1
mov $g0, #0 // |g0|=0
mov $f1, #0 // |f1|=0
mov $g1, #1 // |g1|=1
.Loop_62_256:
sbfx @t[3], $a_lo, #0, #1 // if |a_| is odd, then we'll be subtracting
sub $cnt, $cnt, #1
and @t[0], $b_lo, @t[3]
sub @t[1], $b_lo, $a_lo // |b_|-|a_|
subs @t[2], $a_lo, @t[0] // |a_|-|b_| (or |a_|-0 if |a_| was even)
mov @t[0], $f0
csel $b_lo, $b_lo, $a_lo, hs // |b_| = |a_|
csel $a_lo, @t[2], @t[1], hs // borrow means |a_|<|b_|, replace with |b_|-|a_|
mov @t[1], $g0
csel $f0, $f0, $f1, hs // exchange |f0| and |f1|
csel $f1, $f1, @t[0], hs
csel $g0, $g0, $g1, hs // exchange |g0| and |g1|
csel $g1, $g1, @t[1], hs
lsr $a_lo, $a_lo, #1
and @t[0], $f1, @t[3]
and @t[1], $g1, @t[3]
add $f1, $f1, $f1 // |f1|<<=1
add $g1, $g1, $g1 // |g1|<<=1
sub $f0, $f0, @t[0] // |f0|-=|f1| (or |f0-=0| if |a_| was even)
sub $g0, $g0, @t[1] // |g0|-=|g1| (or |g0-=0| ...)
cbnz $cnt, .Loop_62_256
ret
.size __inner_loop_62_256,.-__inner_loop_62_256
___
}
foreach(split("\n",$code)) {
s/\b(smaddl\s+x[0-9]+,\s)x([0-9]+,\s+)x([0-9]+)/$1w$2w$3/;
print $_,"\n";
}
close STDOUT;
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